Skip to main content
×
Home
    • Aa
    • Aa
  • Access
  • Cited by 28
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Ueki, Sei-ichiro 2016. Higher Order Derivative Characterization for Fock-Type Spaces. Integral Equations and Operator Theory, Vol. 84, Issue. 1, p. 89.


    El-Sayed Ahmed, A. 2014. Characterizations for General Besov-Type Space in Clifford Analysis. Advances in Applied Clifford Algebras, Vol. 24, Issue. 4, p. 1011.


    Ueki, Sei-Ichiro 2014. Characterization for Fock-Type Space via Higher Order Derivatives and its Application. Complex Analysis and Operator Theory, Vol. 8, Issue. 7, p. 1475.


    Chaisuriya, Pachara Reséndis O, Lino F. Tovar S., Luis M. and Zhao, Ruhan 2013. A new class of analytic function with measures. Complex Variables and Elliptic Equations, Vol. 58, Issue. 8, p. 1145.


    Miss Paredes, Augusto Guadalupe Reséndis Ocampo, Lino Feliciano and Tovar Sánchez, Luis Manuel 2013. Holomorphic Spaces in the Unit Ball of. Journal of Function Spaces and Applications, Vol. 2013, p. 1.


    Ahmed, Ahmed and Kamal, Alaa 2012. Generalized composition operators on QK,ω (p,q) spaces. Mathematical Sciences, Vol. 6, Issue. 1, p. 14.


    Reséndis, L.F. and Tovar, L.M. 2012. 𝒬psubharmonic classes in the unit ball of ℝn. Complex Variables and Elliptic Equations, Vol. 57, Issue. 7-8, p. 867.


    El-Sayed Ahmed, A. 2010. Lacunary Series in Weighted HyperholomorphicBp,q(G) Spaces. Numerical Functional Analysis and Optimization, Vol. 32, Issue. 1, p. 41.


    Harutyunyan, Anahit V. and Harutyunyan, Gohar 2010. Holomorphic Besov spaces in the polydisc and bounded Toeplitz operators. Analysis, Vol. 30, Issue. 4,


    Harutyunyan, A. V. and Lusky, W. 2010. Duals of holomorphic Besov spaces on the polydisks and diagonal mappings. Journal of Contemporary Mathematical Analysis, Vol. 45, Issue. 3, p. 128.


    Ye, Shanli 2010. A WEIGHTED COMPOSITION OPERATOR ON THE LOGARITHMIC BLOCH SPACE. Bulletin of the Korean Mathematical Society, Vol. 47, Issue. 3, p. 527.


    El-Sayed Ahmed, A. 2009. Lacunary series in quaternion Bp,qspaces. Complex Variables and Elliptic Equations, Vol. 54, Issue. 7, p. 705.


    LI, SONGXIAO WULAN, HASI ZHAO, RUHAN and ZHU, KEHE 2009. A CHARACTERISATION OF BERGMAN SPACES ON THE UNIT BALL OF ℂn. Glasgow Mathematical Journal, Vol. 51, Issue. 02, p. 315.


    Ahmed, A. El-Sayed 2008. On Weighted α-Besov Spaces and α-Bloch Spaces of Quaternion-Valued Functions. Numerical Functional Analysis and Optimization, Vol. 29, Issue. 9-10, p. 1064.


    Li, Songxiao and Stević, Stevo 2008. Some characterizations of the Besov space and the α-Bloch space. Journal of Mathematical Analysis and Applications, Vol. 346, Issue. 1, p. 262.


    El-Sayed Ahmed, A. Gürlebeck, K. Reséndis, L. F. and Tovar S., Luis M. 2006. Characterizations for Bloch space by Bp, qspaces in Clifford analysis. Complex Variables and Elliptic Equations, Vol. 51, Issue. 2, p. 119.


    Kwon, E.G. 2006. A characterization of Bloch space and Besov space. Journal of Mathematical Analysis and Applications, Vol. 324, Issue. 2, p. 1429.


    Kwon, Ern-Gun Shim, Ok-Hee and Bae, Eun-Kyu 2006. A CHARACTERIZATION OF BLOCH FUNCTIONS. Communications of the Korean Mathematical Society, Vol. 21, Issue. 2, p. 287.


    Rättyä, J. 2003. n-th derivative characterisations, mean growth of derivatives and F( p, q, s). Bulletin of the Australian Mathematical Society, Vol. 68, Issue. 03, p. 405.


    Gürlebeck, K. and Malonek, H. R. 2001. On strict inclusions of weighted dirichlet spaces of monogenic functions. Bulletin of the Australian Mathematical Society, Vol. 64, Issue. 01, p. 33.


    ×
  • Bulletin of the Australian Mathematical Society, Volume 39, Issue 3
  • June 1989, pp. 405-420

Besov-type characterisations for the Bloch space

  • Karel Stroethoff (a1)
  • DOI: http://dx.doi.org/10.1017/S0004972700003324
  • Published online: 17 April 2009
Abstract

We will prove local and global Besov-type characterisations for the Bloch space and the little Bloch space. As a special case we obtain that the Bloch space consists of those analytic functions on the unit disc whose restrictions to pseudo-hyperbolic discs (of fixed pseudo-hyperbolic radius) uniformly belong to the Besov space. We also generalise the results to Bloch functions and little Bloch functions on the unit ball in . Finally we discuss the related spaces BMOA and VMOA.

    • Send article to Kindle

      To send this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Besov-type characterisations for the Bloch space
      Your Kindle email address
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      Besov-type characterisations for the Bloch space
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      Besov-type characterisations for the Bloch space
      Available formats
      ×
Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[2]J. Arazy and S.D. Fisher , ‘Some aspects of the minimal, Möbius-invariant spaces of analytic functions on the unit disc’, pages 2444, in Interpolation Spaces and Allied Topics in Analysis, edited by M. Cwikel and J. Peetre (Lecture Notes in Mathematics, 1070, Springer-Verlag, Berlin-New York, 1984).

[4]S. Axler , ‘The Bergman Space, The Bloch Space and Commutators of Multiplication Operators’, Duke Math. J. 53 (1986), 315332.

[8]L.A. Rubel and R.M. Timoney , ‘An extremal property of the Bloch space’, Proc. Amer. Math. Soc. 75 (1979), 4549.

[9]W. Rudin , Function Theory in the Unit Ball of ℂN (Springer-Verlag, New York, 1980).

[10]R.M. Timoney , ‘Bloch functions in several complex variables, I’, Bull. London Math. Soc. 12 (1980), 241267.

[11]K. Zhu , ‘The Bergman Spaces, the Bloch Space, and Gleason's Problem’, Trans. Amer. Math. Soc. 309 (1988), 253268.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax